You can find a dome fossil one of two ways:
1. FireRed and LeafGreen: When you get to the end of Mt. Moon you will be givin a choice of two fossils: Dome or Helix
2. Platinum, Pearl, Diamond: You can find Dome Fossils along with Helix, Claw, Root, Skull, and Armor Fossils and Old Amber in the Underground. If you do not have the National Dex, then only the Skull and Armor Fossils will appear.